The invention disclosed and claimed herein is generally directed to a method for correcting spatial inhomogeneity or nonuniformity of spatial intensity in an acquired magnetic resonance (MR) or other medical diagnostic image. More particularly, the invention is directed to a correction method of such type wherein the primary component of inhomogeneity is slowly varying.
In many areas of imaging including MR and computed tomography, acquired images are corrupted by slowly varying multiplicative inhomogeneities or nonuniformities in spatial intensity. Such nonuniformities can hinder visualization of the entire image at a given time, and can also hinder automated image analysis. Such inhomogeneity is a particular concern in MR when single or multiple surface coils are used to acquire imaging data. The acquired images generally contain intensity variations resulting from the inhomogeneous sensitivity profiles of the surface coil or coils. In general, tissue next to the surface coil appears much brighter than tissue far from the coil. Spatial intensity variations introduced by surface coil nonuniformity hinders visualization because one cannot find a window/level adjustment to encompass the entire field of view. When such images are filmed, the operator tries to select a setting which covers most of the features of interest. Furthermore, uncorrected image inhomogeneity makes it difficult to perform image segmentation and other aspects of image analysis.
An example of the problem is spine imaging, wherein one or more surface coils are placed behind a patient. If the central spinal canal is filmed optimally, tissue structure behind the vertebral column may be overamplified and may become so bright that no tissue detail can be seen. At the same time, tissue in front of the vertebral column may be so dark that image detail in that area is also obscured. Therefore, in order to optimally display and film the entire image, the signal variation due to the inhomogeneous sensitivity profile of the surface coil needs to be corrected. Surface coil image signal intensities generally represent the product of (1) precessing magnetization of the body tissue or other object being imaged, and (2) the sensitivity profile of the surface coil. Accordingly, various intensity correction algorithms have been devised to correct surface coil images by dividing out an estimate of the surface coil's sensitivity profile. Thus, if the observed or acquired MR image signal is defined in a spatial domain for a voxel location (x,y,z) by the function g(x,y,z) then g(x,y,z)=h(x,y,z)*f(x,y,z)+n(x,y,z), where * represents multiplication, h.function., and n represent the coil profile function, a corrected function, and the imaging noise, respectively. More specifically, the corrected function .function. is a function defining an image which is substantially free of distortion resulting from the inhomogeneity. Thus, the problem is to determine both h and .function., given only the measured or acquired function g in the presence of n. However, if the function h can be determined which reasonably represents the inhomogeneity distortion, then .function. can be readily computed from ##EQU1## which is known in the art as Weiner filter solution, where .psi..sub.1 is a regularization parameter corresponding to the reciprocal of signal to noise ratio. Herein, and in the following discussion, location indices (x,y,z) have been dropped for the sake of brevity.
The distortion arising from use of surface coils generally varies slowly over space. An important class of prior art solutions to the above problem is based on this assumption. In accordance therewith, a low pass filtering operation is applied to g. The resulting function, represented as LPFg!, does not contain high frequency components and is taken as an estimate of distortion function h. An estimate of .function. is then obtained by dividing g by LPFg!, i.e., .function.=g/LPFg!. However, for this class of methods to be effective, g must not contain sharp intensity transitions. Unfortunately, in MR imaging an air-lipid interface usually contains sharp intensity transitions which violate the basic assumption made in the method, i.e., that the low frequency content in the scene being imaged is solely due to h. Significant air-lipid interferences will generally be encountered, for example, at the edges of an organ, i.e., at the boundary between the organ and an air-space or cavity.
To overcome the above deficiency in low pass filtering correction at the edge or boundary of an organ or other tissue structure, certain hybrid filtering techniques have been developed. Some of such techniques are set forth in the following references: Surface Coil MR Imaging of the Human Brain with an Analytic Reception Profile Correction, JMRI 5, 139-144, by S. E. Moyher, D. B. Vigeron, and S. J. Nelson; Phased Array Detectors and an Automated Intensity Correction Algorithm for High Resolution MR Imaging of the Human Brain, JMRI (1995), by L L. Wald, L. Carvajal, S. E. Moyher, S. J. Nelson, P. E. Grant, A. J. Barkovich, and D. B. Vingeron; and Phased Array Image Intensity Correction: An Algorithm to Remove Intensity Variations in MR Images Resulting from the Inhomogeneous Sensitivity Profiles of Phased Array Surface Coils, a Master's thesis by J. Murakami (1995), University of Washington, Seattle.
In a further reference, entitled Intensity Correction of Phased-Array Surface Coil Images, MRM 35:585-590 (1996), by Murakami et al, a technique is disclosed wherein the distortion function h is set to h=LPFg!/LPFTHRESHg!!. THRESH g! is a thresholded or threshold operation, wherein intensity values of respective pixels of the acquired function g are compared with a threshold value set at a noise level. Intensity values above the noise level are assigned a level equal to the average intensity of the image, and the remaining intensity values are set to zero.
The thresholding operation has the effect of smoothing the distortion function h at the boundaries or edge regions of organs and other tissue structures, which result from the substantial intensity transitions occurring at such regions. This is because THRESHg! will be greater at such regions, and accordingly will reduce LPF g!. However, neither the technique of Murakami nor other hybrid filtering techniques is particularly effective in accounting for significant internal transitions, i.e., transitions which occur between the edges of an organ or other tissue structure. Moreover, such internal transitions are determined by the tissue of a particular patient, rather than by the parameters of the MR equipment. Accordingly, it would be very desirable to develop a form for a distortion function h which is substantially unaffected by the tissue structure of a particular patient, and by abrupt transitions occurring therein. Furthermore, it would be desirable to speed up the computations without sacrificing accuracy.